Since then, numerous other bounds for \(E(G)\)  were discovered, see [1]}, [2]}, [3]}, [4]}.
In [5]} Koolen and Moulton improved the bound (REF ) as follows: If \(2m>n\)  and \(G\)  is a graph with \(n\)  vertices and \(m\)  edges, then
\(E(G)\le \frac{2m}{n}+\sqrt{(n-1)\left(2m-\left(\frac{2m}{n}\right)^{2}\right)}.\) 
